How does the electric field make a droplet exhibit the ejection and rebound behaviour on a superhydrophobic surface?

A droplet impinging on a superhydrophobic substrate in an electric field is an important process in droplet manipulation and electrostatic spraying. Here, the entire impinging dynamic of the droplet in a vertical electric field is studied by a visualization experiment and numerical simulation with OpenFOAM. We investigate the effect of an electrostatic force on droplet impact in depth, where four ejection modes and three rebound modes are found experimentally. In particular, the filamentous ejecting phenomenon occurs after a droplet impinging on a superhydrophobic substrate is first discovered. In the numerical simulation, the strong coupling between the dynamic distribution of the interface electric charge and the evolution of the droplet profile can lead to different ejection modes, and the different ejection behaviours are caused by the combined effects of electrostatic pressure, capillary pressure, dynamic pressure and static pressure on the droplet apex. A charge scaling law for the ejection droplets is proposed. Furthermore, a set of theoretical models is established, which can successfully predict the threshold electric capillary number for different droplet ejection modes. The results reveal some important characteristics for a droplet impinging on a superhydrophobic surface in an electric field, which could facilitate the design of electrically operated droplet equipment and guide the safe and stable operation of the device.